Maybe not. A 2011 study published in Human Relations surveyed 60,000 full-time workers on their attitudes toward male versus female managers. At first, its conclusions seem to bolster Sandberg’s claim that people are more accepting of successful men than successful women: Of the 46 percent of respondents who expressed a preference for their boss’s gender, 72 percent said they wanted a male manager. But another aspect of the results highlights a flaw in the Heidi/Howard study: People who actually had female managers did not give them lower ratings than people who had male managers. That is, though many people preferred male managers in theory, in practice those gender biases did not play out.

There’s a precedent for this, of course. Humans tend to be opposed to changes in the status quo until they are forced, through experience, to see that change isn’t such a big deal. Marriage equality advocates have learned this lesson well. Before last fall’s string of ballot victories, pro-gay marriage groups ran ads depicting happy, committed gay couples and testimonies from “straight, respected people from unexpected corners of the community, like a firefighter in Maine,” as the New York Times put it. These ads reflected the understanding that for some people, same-sex marriage may be scary in theory, but once they get to know real gay couples, it’s not scary at all–it’s actually desirable.

It looks like this is happening, and will continue to happen, with female leaders.